I know exactly what you are talking about with the shaking, I have a set of heavy castors left over from another project but after seeing my 2006 run I have decided to not use them. In fact I have clamped my machine to the permanent bench with sections of 1x4's which has eliminated the shake.
I'd say that the first order of business for you is to get your machine off the wheels and provide a solid connection to the floor (which you say that you can't do).
Another area to look at is the length of your legs, in your case shorter would be better right up to no legs at all. Unless you can make some kind of connections to solid members then you may have to slow the machine down to manage the shaking.
I can't answer #2 but have to commend your relation to the jolly fat man in red. Can you put in a good word for me for next year?
Good Luck and HNY,